






"""simple docstring"""
import numpy as np


def 							A						(				__snake_case: np.ndarray ,     __snake_case: np.ndarray ,     __snake_case: float = 1E-12 ,     __snake_case: int = 1_0_0 ,     )    ->		tuple[float, np.ndarray]:

       """simple docstring"""





       assert np.shape(__snake_case  )[0] == np.shape(__snake_case  )[1]
       # Ensure proper dimensionality.
       assert np.shape(__snake_case  )[0] == np.shape(__snake_case  )[0]
       # Ensure inputs are either both complex or both real
       assert np.iscomplexobj(__snake_case  ) == np.iscomplexobj(__snake_case  )
       __magic_name__      				=    np.iscomplexobj(__snake_case  )
       if is_complex:
              # Ensure complex input_matrix is Hermitian
              assert np.array_equal(__snake_case ,     input_matrix.conj().T  )

       # Set convergence to False. Will define convergence when we exceed max_iterations
       # or when we have small changes from one iteration to next.

       __magic_name__      				=    False
       __magic_name__      				=    0
       __magic_name__      				=    0
       __magic_name__      				=    1E12

       while not convergence:
              # Multiple matrix by the vector.
              __magic_name__      				=    np.dot(__snake_case ,     __snake_case  )
              # Normalize the resulting output vector.
              __magic_name__      				=    w / np.linalg.norm(__snake_case  )
              # Find rayleigh quotient
              # (faster than usual b/c we know vector is normalized already)
              __magic_name__      				=    vector.conj().T if is_complex else vector.T
              __magic_name__      				=    np.dot(__snake_case ,     np.dot(__snake_case ,     __snake_case  )  )

              # Check convergence.
              __magic_name__      				=    np.abs(lambda_ - lambda_previous  ) / lambda_
              iterations += 1

              if error <= error_tol or iterations >= max_iterations:
                     __magic_name__      				=    True

              __magic_name__      				=    lambda_

       if is_complex:
              __magic_name__      				=    np.real(lambda_  )

       return lambda_, vector


def 							A						(				)    ->		None:

       """simple docstring"""





       __magic_name__      				=    np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]  )
       __magic_name__      				=    np.array([4_1, 4, 2_0]  )
       __magic_name__      				=    real_input_matrix.astype(np.complexaaa  )
       __magic_name__      				=    np.triu(1J * complex_input_matrix ,     1  )
       complex_input_matrix += imag_matrix
       complex_input_matrix += -1 * imag_matrix.T
       __magic_name__      				=    np.array([4_1, 4, 2_0]  ).astype(np.complexaaa  )

       for problem_type in ["real", "complex"]:
              if problem_type == "real":
                     __magic_name__      				=    real_input_matrix
                     __magic_name__      				=    real_vector
              elif problem_type == "complex":
                     __magic_name__      				=    complex_input_matrix
                     __magic_name__      				=    complex_vector

              # Our implementation.
              __magic_name__				,  __magic_name__      				=    power_iteration(__snake_case ,     __snake_case  )

              # Numpy implementation.

              # Get eigenvalues and eigenvectors using built-in numpy
              # eigh (eigh used for symmetric or hermetian matrices).
              __magic_name__				,  __magic_name__      				=    np.linalg.eigh(__snake_case  )
              # Last eigenvalue is the maximum one.
              __magic_name__      				=    eigen_values[-1]
              # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
              __magic_name__      				=    eigen_vectors[:, -1]

              # Check our implementation and numpy gives close answers.
              assert np.abs(eigen_value - eigen_value_max  ) <= 1E-6
              # Take absolute values element wise of each eigenvector.
              # as they are only unique to a minus sign.
              assert np.linalg.norm(np.abs(__snake_case  ) - np.abs(__snake_case  )  ) <= 1E-6


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 test_power_iteration()







"""simple docstring"""
from ..utils import DummyObject, requires_backends



class        UpperCamelCase__ (				metaclass=a_):







    """simple docstring"""
    __UpperCAmelCase           = ["""flax""", """transformers"""]







    def __init__(		self :	List[Any]				,    *UpperCamelCase_ :	str				,    **UpperCamelCase_ :	Any ):





           '''simple docstring'''

           requires_backends(self				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	Optional[int]				,    *UpperCamelCase_ :	Tuple				,    **UpperCamelCase_ :	List[Any] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	str				,    *UpperCamelCase_ :	Optional[Any]				,    **UpperCamelCase_ :	Dict ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )



class        UpperCamelCase__ (				metaclass=a_):







    """simple docstring"""
    __UpperCAmelCase           = ["""flax""", """transformers"""]







    def __init__(		self :	List[Any]				,    *UpperCamelCase_ :	str				,    **UpperCamelCase_ :	str ):





           '''simple docstring'''

           requires_backends(self				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	Optional[int]				,    *UpperCamelCase_ :	Optional[int]				,    **UpperCamelCase_ :	List[str] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	Tuple				,    *UpperCamelCase_ :	List[str]				,    **UpperCamelCase_ :	Optional[Any] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )



class        UpperCamelCase__ (				metaclass=a_):







    """simple docstring"""
    __UpperCAmelCase           = ["""flax""", """transformers"""]







    def __init__(		self :	Optional[int]				,    *UpperCamelCase_ :	List[Any]				,    **UpperCamelCase_ :	List[str] ):





           '''simple docstring'''

           requires_backends(self				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	str				,    *UpperCamelCase_ :	List[str]				,    **UpperCamelCase_ :	Tuple ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	Tuple				,    *UpperCamelCase_ :	Any				,    **UpperCamelCase_ :	List[str] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )



class        UpperCamelCase__ (				metaclass=a_):







    """simple docstring"""
    __UpperCAmelCase           = ["""flax""", """transformers"""]







    def __init__(		self :	Optional[Any]				,    *UpperCamelCase_ :	Optional[Any]				,    **UpperCamelCase_ :	Dict ):





           '''simple docstring'''

           requires_backends(self				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	str				,    *UpperCamelCase_ :	Dict				,    **UpperCamelCase_ :	List[str] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )







    @classmethod
    def 				a__			(		cls :	str				,    *UpperCamelCase_ :	Optional[Any]				,    **UpperCamelCase_ :	Union[str, Any] ):





           '''simple docstring'''

           requires_backends(cls				,    ['flax', 'transformers'] )